Discrete Math - 9.1.2 Properties of Relations

Exploring the properties of relations including reflexive, symmetric, anti-symmetric and transitive properties.

Video Chapters:
Introduction 0:00
Reflexive Relations 0:07
Symmetric Relations 1:56
Anti-Symmetric Relations 4:11
Transitive Relations 9:27
Relation Properties Practice 14:55
Up Next 21:35

Textbook: Rosen, Discrete Mathematics and Its Applications, 7e

[valeriereid]

Finally, I understand the antisymmetric property. Thank you Professor Brehm.

[shivrajkaushik]

anti-symmetric is very complicated
wasn't able to understand completely but the rest of all was totally clear and for that a big

[punditgi]

I can really relate to what Kimberly is teaching! 😃

[michellebalopi]

i love how you follow through with the same example from the previous video. 😊❤

[supervideojugadores]

amazing content! si glad that yt brought me here

[megancornwall]

Hi, in the last example, when we heck for the transitive property, why don't we test (3, 3) and other pairs?

[ehclipse]

At 9:20
I am still confused about how R_3 is anti-symmetric.
I understand that 0 -> 1 is true. But I can't think of an example for R_3 where a = b, which confuses me.

[coryanders]

The antisymmetric property is explained as being the exact same thing as the symmetric property. Why are they considered different from one another?

[somilarora]

at 14:45 we can also take an example for (a + b <- 3) which is (1, 2), (2, 0) --- (1, 0) so hence proved that it's valid for all 4

[mirainuko]

I was confused with anti-symmetric relations until I looked at the contrapositive. If a relation is antisymmetric, then for all a & b in A: If (a != b) then not ( ((a, b) is in R) and ((b, a) is in R) ). In other words, in an anti-symmetric relation, you can never have a pair of distinct a, b such that both (a, b) and (b, a) are in the relation.

[bestyoueverhad.]

Would really appreciate it, if you could help, explain the Asymmetric and Irreflexive Relations properties.

[curious]

Either R2 is wrong or R4 is wrong. Please recheck

[skaldrun]

Hi, in the last example, when we heck for the transitive property, why don't we test (3, 3) and other pairs? Because if we find one counter example, it wouldnt be a transitive. And there is a counter example for (3, 3).

[curious]

in R4 why can't we just make a & b = 0 or 1? then it would be true

[stevenfarrel]

What happen if the number that we looking for is not in relations? for example suppose my roster method is {(-2, 4), (0, 0), (2, 4)} Basically we're looking for the number that it is end with 4. However there is no anything that start with 4 like{4, 2} and so on is it okay if we can say that it is transitive?

[zenemy]

(1, 1) and (3, 3) so (1, 3) does not belong in the set R

[leon]

3:50 if I choose 3 and 4 how it can be true?

[gk_zzz]

hi question in the relation number 4 in the anti-symmetric part what if we have (0, 0) ?

[leogao]

for antisemmetric, In R3 q is false, a does not equal b, because q is false and p is false p->q is true, so don't listen to her